SAN FRANCISCO — Broadcom on Monday proposed a slate of 11 directors to replace the entire board of Qualcomm, setting the stage for a proxy battle over the fate of its unsolicited $105 billion bid for the world’s largest maker of smartphone chips.

The proposal was widely seen as a tactic to pressure Qualcomm to negotiate what would be the largest technology deal in history. Last month, Qualcomm said its directors had unanimously rejected the bid that Broadcom had announced in early November, leaving Broadcom with the option to take the issue to shareholders by proposing a board slate who would back it.

Qualcomm on Monday criticized Broadcom’s latest move, calling it a “blatant attempt” to seize control of the board to advance an acquisition offer Qualcomm said drastically undervalued the company.

Broadcom’s gambit adds a new dimension to a struggle with immensely high stakes. If completed, a combination of Broadcom and Qualcomm would top the $67 billion that Dell paid for the data storage specialist EMC in 2016, the previous record-setting deal in the sector.

Besides the huge potential price tag of a transaction, the contest has implications for a business model in the chip industry that has been both lucrative and controversial. Qualcomm had built itself into a mobile-chip giant by charging patent royalties to smartphone makers, in addition to selling them chips, under terms that have prompted opposition from customers like Apple and some regulators.

Hock E. Tan, Broadcom’s chief executive, is likely to argue that it is time to change Qualcomm’s patent-licensing practices. He has won many fans on Wall Street already by wringing profits from a series of companies he has acquired, a strategy that has strengthened Broadcom’s market value.

“What Broadcom is saying to Qualcomm is, ‘Your old way of doing business is done,’” said Stacy Rasgon, an analyst at Sanford C. Bernstein.

Qualcomm has defended its business model, which it studied in depth in 2015 as part of its response to pressure from the activist investor Jana Partners. The investment firm won the right to name three Qualcomm board members as part of a settlement with the company, which cut $1.4 billion in expenses that year to help bolster profitability.

Qualcomm has set March 6 as the date for an annual shareholders meeting, which will include the election of directors. Proxy materials associated with the slates of candidates from Qualcomm and Broadcom are likely to be distributed in January.

In seeking to oust Qualcomm’s entire board, Broadcom is using one of the few means at its disposal to force a start to negotiations. Broadcom had hoped to strike friendly negotiations, but the company said Qualcomm’s management and board had shown little interest in deal talks.

“We have repeatedly attempted to engage with Qualcomm, and despite stockholder and customer support for the transaction, Qualcomm has ignored those opportunities,” Mr. Tan said in a statement.

The 11 nominees include executives with either operating or board experience with companies that sell semiconductors or other high-tech products. They include John Kispert, former chief executive of Spansion; Gregorio Reyes, a former chairman at LSI and Dialog Semiconductor; Samih Elhage, who held several senior positions at Nokia; Thomas Volpe, a former director at Linear Technology who is managing member of Volpe Investments; and Harry L. You, a former executive at EMC and Oracle.

Broadcom also offered to expand the Qualcomm board by retaining the three existing directors who were named by Jana.

Qualcomm called Broadcom’s board nominees “inherently conflicted given Broadcom’s desire to acquire Qualcomm in a manner that dramatically undervalues Qualcomm to Broadcom’s benefit.” It stressed its directors were willing to objectively evaluate “the full range of opportunities available to maximize value for all Qualcomm stockholders.”

The two chip makers had talked earlier. Mr. Tan disclosed in a letter to Qualcomm’s board that he had discussed a combination in August 2016 with Steve Mollenkopf, Qualcomm’s chief executive.

People familiar with the situation, who spoke on the condition of anonymity because the details are confidential, said Mr. Mollenkopf met with Mr. Tan more than once and Qualcomm hired external advisers to review a possible transaction. Because Broadcom’s market value was considerably smaller than it is now, any deal might have been a merger or acquisition by Qualcomm, these people said.

As it turned out, Qualcomm opted to expand its business last year with a $38.5 billion deal to acquire NXP Semiconductors. That transaction, which is awaiting regulatory approval that could come early next year, could impact how much Broadcom could pay for Qualcomm.

Broadcom has offered $70 a share, a price it said represented a 28 percent premium over the closing price of Qualcomm’s common stock before reports of a potential bid. Qualcomm has argued that the current bid was too low even as a starting point for negotiations, but Broadcom contends its offer was the most significant catalyst for Qualcomm’s stock price in nearly a year. Its shares had traded below $60 a share for most of the year before Broadcom announced its offer.

How much support Broadcom has from Qualcomm investors remains unclear. Shares in the chip maker declined less than 2 percent on Monday, an indication that shareholders are not confident a deal will take place. Broadcom could try to initiate deal negotiations by raising its bid, but it is unclear if it would try to do so before the March 6 shareholders meeting.

Broadcom is scheduled to announce quarterly earnings on Wednesday afternoon, and it may discuss its plans regarding Qualcomm during a scheduled conference call.

Any purchase of Qualcomm would almost certainly face a lengthy regulatory review. Besides antitrust concerns, the possibility of sensitive American technology falling into foreign hands would be examined closely by the Committee on Foreign Investment in the United States, an agency known as Cfius.

Broadcom, although managed from San Jose, Calif., has its headquarters in Singapore. Mr. Tan pledged before announcing the Qualcomm bid to shift Broadcom’s home base to the United States — a move that might help it evade a Cfius review — but no further action to move its headquarters has been announced.

People with knowledge of Broadcom’s deliberations said that the company had met with several regulators and felt comfortable that a deal would win approval.

Don Clark reported from San Francisco and Michael de la Merced from London.

A version of this article appears in print on , on Page B3 of the New York edition with the headline: Broadcom Urges Ousting Qualcomm Board as Takeover Fight Heats Up. Order Reprints | Today’s Paper | Subscribe